Question

Which ordered pair is NOT a solution to the inequality in the graph? (5,1) (4,6) (0,0) (-2,-8)

Answer 1

Answer:  (5,1)

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Explanation:

The red shaded region is the solution set. In other words, if the point is in the red region, then it is a solution. A point like (0,0) is in the red area, so we cross that off the list. The same applies for (4,6) and (-2,-8) as well.

In contrast, a point like (5,1) is not in the red shaded area, so this point is not a solution. Hence it's the final answer.

Note: the solid boundary line means points on the boundary are considered solutions. A dashed boundary line would be used to exclude boundary points from the solution set. Solid boundary lines always go with "or equal to".

Refer to the drawing below if you need a visual of what's going on. I've plotted the four points on the graph given.

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Here's an algebraic approach if you don't have a graph and only have the inequality. Ignore this section if you prefer the first section above.

If we plugged (x,y) = (0,0) into the inequality, then we get...

$y \ge 2x-4\\\\0 \ge 2(0)-4\\\\0 \ge 0-4\\\\0 \ge -4$

That's a true statement because 0 is to the right of -4 on the number line, making 0 larger than -4. Since the last inequality is true, this makes the first inequality true. Furthermore, it algebraically confirms why (0,0) is a solution. You should find that (4,6) and (-2,-8) will lead to true statements as well, so they are solutions.

In contrast, (x,y) = (5,1) is not a solution because...

$y \ge 2x-4\\\\1 \ge 2(5)-4\\\\1 \ge 10-4\\\\1 \ge 6$

which is false. The value 1 is not larger than 6, nor is it equal to 6.